Field x Level x Handedness (binned)
Do we find an interaction of field x level x handedness, when
handedness is binned as left (EHI <= -40) or right (EHI > +40)?
Summary. For reaction time, we find the
critical interaction in the predicted direction (11.67ms, 95% CI [0.65,
22.69], p = .019, one-sided). Left handers show 15.64ms LVF global bias
(95% CI [7.61, 23.67]), and right handers 27.31ms (95% CI [19.80,
34.81]). Mixed handers (not included in the categorical interaction
analysis) show a LVF global bias of 21.66ms (95% CI [9.09, 34.23]).
For accuracy, we find no significant interaction of field by level by
handedness (OR = 0.90, 95% CI [0.70, 1.16], p = .42; where OR < 1
means greater LVF global bias for left handers). Point estimates of LVF
global bias hardly differ between left handers (OR = 1.95, 95% CI [1.62,
2.35]) and right handers (OR = 1.77, 95% CI [1.49, 2.10]). For mixed
handers (not included in the categorical interaction analysis), the
point estimate is 1.10 (95% CI [0.82, 1.47])
Reaction time
Plots
Error bars show 95% CI.



Statistics
Simple mixed regression model
Reaction time is modeled as a linear effect of field, level, and
handedness, using data from every target-present trial with a “go”
response:
lmer( rt ~ field*level*handedness + (1 | subject) )
| npar |
AIC |
BIC |
logLik |
deviance |
Chisq |
Df |
p.value |
| 9 |
1,166,282.858 |
1,166,367.139 |
−583,132.429 |
1,166,264.858 |
- |
- |
- |
| 10 |
1,166,280.551 |
1,166,374.197 |
−583,130.276 |
1,166,260.551 |
4.307 |
1 |
.038 |
| field_consec |
level_consec |
handedness_consec |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF - RVF |
Local - Global |
Right - Left |
11.666 |
5.622 |
Inf |
0.648 |
22.685 |
2.075 |
.038 |
| field_consec |
level_consec |
handedness |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF - RVF |
Local - Global |
Left |
15.641 |
4.096 |
Inf |
7.613 |
23.669 |
3.819 |
.0001 |
| LVF - RVF |
Local - Global |
Mixed |
21.658 |
6.414 |
Inf |
9.087 |
34.228 |
3.377 |
.0007 |
| LVF - RVF |
Local - Global |
Right |
27.307 |
3.829 |
Inf |
19.802 |
34.812 |
7.131 |
<.0001 |
| term |
df |
sumsq |
meansq |
statistic |
p.value |
| field |
1 |
1,664,691.722 |
1,664,691.722 |
23.612 |
<.0001 |
| level |
1 |
9,626,122.373 |
9,626,122.373 |
136.54 |
<.0001 |
| handedness |
1 |
10,185,712.46 |
10,185,712.46 |
144.477 |
<.0001 |
| field:level |
1 |
2,730,949.837 |
2,730,949.837 |
38.737 |
<.0001 |
| field:handedness |
1 |
1,505,316.949 |
1,505,316.949 |
21.352 |
<.0001 |
| level:handedness |
1 |
12,247.994 |
12,247.994 |
0.174 |
.677 |
| field:level:handedness |
1 |
127,954.685 |
127,954.685 |
1.815 |
.178 |
| Residuals |
86,205 |
6,077,502,195.866 |
70,500.576 |
- |
- |
summary(rt_model_2bins)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field * level * handedness + (1 | subject)
## Data: aah_for_rt_model_2bins
##
## REML criterion at convergence: 1166226.1
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.871042 -0.589962 -0.165354 0.361143 7.634801
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 28355.6 168.391
## Residual 42345.3 205.780
## Number of obs: 86213, groups: subject, 709
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 663.50167 9.47901 69.99697
## fieldLVF -25.29475 2.87911 -8.78560
## levelLocal 13.71496 2.91027 4.71261
## handednessRight 18.61377 12.98209 1.43380
## fieldLVF:levelLocal 15.64117 4.10675 3.80865
## fieldLVF:handednessRight 10.27036 3.94550 2.60306
## levelLocal:handednessRight -6.47365 3.98194 -1.62575
## fieldLVF:levelLocal:handednessRight 11.66629 5.62176 2.07520
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlLcl hnddnR flLVF:L fLVF:R lvlL:R
## fieldLVF -0.153
## levelLocal -0.152 0.499
## hnddnssRght -0.730 0.112 0.111
## fldLVF:lvlL 0.107 -0.701 -0.707 -0.078
## fldLVF:hndR 0.112 -0.730 -0.364 -0.153 0.512
## lvlLcl:hndR 0.111 -0.365 -0.731 -0.152 0.517 0.500
## fldLVF:lL:R -0.079 0.512 0.517 0.108 -0.731 -0.702 -0.707
Accuracy
Plots
Error bars show 95% CI.



Statistics
Simple mixed regression model
Accuracy is modeled as a binomial effect of field, level, and
handedness, using binary correct/incorrect data from every
target-present trial:
glmer( correct ~ field*level*handedness + (1 | subject), family = "binomial" )
| npar |
AIC |
BIC |
logLik |
deviance |
Chisq |
Df |
p.value |
| 8 |
32,836.316 |
32,911.643 |
−16,410.158 |
32,820.316 |
- |
- |
- |
| 9 |
32,837.667 |
32,922.41 |
−16,409.833 |
32,819.667 |
0.649 |
1 |
.42 |
| field_consec |
level_consec |
handedness_consec |
odds.ratio |
SE |
df |
asymp.LCL |
asymp.UCL |
null |
z.ratio |
p.value |
| LVF / RVF |
Global / Local |
Right / Left |
0.899 |
0.118 |
Inf |
0.696 |
1.162 |
1 |
−0.814 |
.416 |
| field_consec |
level_consec |
handedness |
odds.ratio |
SE |
df |
asymp.LCL |
asymp.UCL |
null |
z.ratio |
p.value |
| LVF / RVF |
Global / Local |
Left |
1.954 |
0.185 |
Inf |
1.623 |
2.353 |
1 |
7.063 |
<.0001 |
| LVF / RVF |
Global / Local |
Mixed |
1.097 |
0.162 |
Inf |
0.821 |
1.465 |
1 |
0.626 |
.532 |
| LVF / RVF |
Global / Local |
Right |
1.766 |
0.154 |
Inf |
1.488 |
2.095 |
1 |
6.514 |
<.0001 |
summary(acc_model_2bins)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * handedness + (1 | subject)
## Data: aah_for_acc_model_2bins
##
## AIC BIC logLik deviance df.resid
## 32837.7 32922.4 -16409.8 32819.7 90743
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -12.046183 0.123597 0.170659 0.240743 1.070559
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.03569 1.01769
## Number of obs: 90752, groups: subject, 709
##
## Fixed effects:
## Estimate Std. Error z value
## (Intercept) 3.1227080 0.0719596 43.39530
## fieldLVF -0.1101649 0.0563127 -1.95631
## levelGlobal 0.4277909 0.0630223 6.78793
## handednessRight 0.1047397 0.0983966 1.06446
## fieldLVF:levelGlobal 0.6731050 0.0962270 6.99497
## fieldLVF:handednessRight -0.0341608 0.0784866 -0.43524
## levelGlobal:handednessRight -0.1561983 0.0867458 -1.80064
## fieldLVF:levelGlobal:handednessRight -0.1065265 0.1308698 -0.81399
## Pr(>|z|)
## (Intercept) < 2.22e-16 ***
## fieldLVF 0.050429 .
## levelGlobal 0.0000000000113752 ***
## handednessRight 0.287118
## fieldLVF:levelGlobal 0.0000000000026532 ***
## fieldLVF:handednessRight 0.663386
## levelGlobal:handednessRight 0.071759 .
## fieldLVF:levelGlobal:handednessRight 0.415651
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldLVF lvlGlb hnddnR flLVF:G fLVF:R lvlG:R
## fieldLVF -0.410
## levelGlobal -0.361 0.467
## hnddnssRght -0.718 0.301 0.266
## fldLVF:lvlG 0.244 -0.589 -0.656 -0.180
## fldLVF:hndR 0.295 -0.720 -0.338 -0.421 0.426
## lvlGlbl:hnR 0.264 -0.342 -0.730 -0.377 0.481 0.478
## fldLVF:lG:R -0.181 0.436 0.487 0.257 -0.740 -0.605 -0.667
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00965947 (tol = 0.002, component 1)
Field x Level x Handedness
(continuous)
Do we find an interaction of field x level x handedness (continuous
EHI score)?
Summary. For reaction time, we find the
critical interaction in the predicted direction (.067ms per EHI unit,
95% CI [0.003, 0.13], p = .020, one-sided). Estimated global bias is
13.32ms lower for strong left handers (EHI -100: 14.82ms, 95% CI [6.48,
23.17]) than for strong right handers (EHI +100: 28.14ms, 95% CI [20.31,
35.98]).
For accuracy, we find no significant interaction of field by level by
EHI (Beta = 0.0002 logodds per EHI unit, 95% CI [-0.001, 0.002], p =
.81). Estimated LVF global bias hardly differs for strong left handers
(EHI -100: OR = 1.67, 95% CI [1.37, 2.03]) and strong right handers (EHI
+100: OR = 1.73, 95% CI [1.45, 2.07]).
Reaction time
Plots

Statistics
Model RT as a linear effect of field, level, and EHI (continuous):
rt_model_ehi <- lmer( rt ~ field*level*ehi + (1 | subject) )
| npar |
AIC |
BIC |
logLik |
deviance |
Chisq |
Df |
p.value |
| 9 |
1,387,640.958 |
1,387,726.807 |
−693,811.479 |
1,387,622.958 |
- |
- |
- |
| 10 |
1,387,638.71 |
1,387,734.097 |
−693,809.355 |
1,387,618.71 |
4.248 |
1 |
.039 |
| field_consec |
level_consec |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| RVF - LVF |
Global - Local |
0.067 |
0.032 |
Inf |
0.003 |
0.13 |
2.061 |
.039 |
| contrast |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF Local - LVF Global |
0.033 |
0.023 |
Inf |
−0.025 |
0.092 |
1.459 |
.463 |
| RVF Local - RVF Global |
−0.033 |
0.023 |
Inf |
−0.092 |
0.026 |
−1.454 |
.465 |
| field |
level |
ehi.trend |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF |
Local |
0.219 |
0.075 |
Inf |
0.073 |
0.366 |
2.93 |
.003 |
| RVF |
Local |
0.096 |
0.075 |
Inf |
−0.05 |
0.243 |
1.288 |
.198 |
| LVF |
Global |
0.186 |
0.075 |
Inf |
0.039 |
0.332 |
2.487 |
.013 |
| RVF |
Global |
0.13 |
0.075 |
Inf |
−0.017 |
0.276 |
1.734 |
.083 |
| field_consec |
level_consec |
ehi |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| RVF - LVF |
Global - Local |
−100 |
14.822 |
4.257 |
Inf |
6.479 |
23.166 |
3.482 |
.0005 |
| RVF - LVF |
Global - Local |
0 |
21.483 |
2.569 |
Inf |
16.447 |
26.519 |
8.361 |
<.0001 |
| RVF - LVF |
Global - Local |
100 |
28.144 |
3.996 |
Inf |
20.311 |
35.976 |
7.042 |
<.0001 |
| contrast |
ehi |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF Local - LVF Global |
−100 |
29.412 |
3.009 |
Inf |
21.683 |
37.141 |
9.776 |
<.0001 |
| RVF Local - RVF Global |
−100 |
14.59 |
3.016 |
Inf |
6.841 |
22.339 |
4.837 |
<.0001 |
| LVF Local - LVF Global |
0 |
32.743 |
1.816 |
Inf |
28.077 |
37.409 |
18.028 |
<.0001 |
| RVF Local - RVF Global |
0 |
11.26 |
1.82 |
Inf |
6.586 |
15.935 |
6.188 |
<.0001 |
| LVF Local - LVF Global |
100 |
36.074 |
2.824 |
Inf |
28.82 |
43.328 |
12.775 |
<.0001 |
| RVF Local - RVF Global |
100 |
7.93 |
2.83 |
Inf |
0.66 |
15.201 |
2.802 |
.026 |
| field |
level |
ehi |
prediction |
asymp.LCL |
asymp.UCL |
| LVF |
Local |
−100 |
658.263 |
638.967 |
677.559 |
| RVF |
Local |
−100 |
667.869 |
648.575 |
687.163 |
| LVF |
Global |
−100 |
628.851 |
609.576 |
648.126 |
| RVF |
Global |
−100 |
653.279 |
633.997 |
672.561 |
| LVF |
Local |
0 |
680.17 |
668.522 |
691.818 |
| RVF |
Local |
0 |
677.494 |
665.848 |
689.14 |
| LVF |
Global |
0 |
647.427 |
635.791 |
659.063 |
| RVF |
Global |
0 |
666.234 |
654.594 |
677.874 |
| LVF |
Local |
100 |
702.077 |
683.953 |
720.201 |
| RVF |
Local |
100 |
687.119 |
668.998 |
705.24 |
| LVF |
Global |
100 |
666.002 |
647.895 |
684.11 |
| RVF |
Global |
100 |
679.189 |
661.074 |
697.303 |
\[
28.144 - 14.822 = 13.322ms \\
13.322/200 = 0.067ms / EHI unit
\] The model estimates that an average strong right hander (EHI
+100) will have 13.32ms more LVF global bias than a
strong left hander (EHI -100). Each unit change in EHI (-100:100)
corresponds to a 0.067ms difference in LVF global bias.
This is also the slope estimate given by the summary function:
summary(rt_model_ehi)
## Linear mixed model fit by REML ['lmerMod']
## Formula: rt ~ field:level:ehi + field:level + field:ehi + level:ehi +
## field + level + ehi + (1 | subject)
## Data: aah_for_rt_ehi_model
##
## REML criterion at convergence: 1387626.2
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -4.879612 -0.590631 -0.167132 0.363313 7.653749
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 28269.4 168.135
## Residual 42128.7 205.253
## Number of obs: 102615, groups: subject, 844
##
## Fixed effects:
## Estimate Std. Error t value
## (Intercept) 680.1697334 5.9429525 114.44980
## fieldRVF -2.6755865 1.8307862 -1.46144
## levelGlobal -32.7431087 1.8162558 -18.02781
## ehi 0.2190687 0.0747656 2.93007
## fieldRVF:levelGlobal 21.4828945 2.5694569 8.36087
## fieldRVF:ehi -0.1228165 0.0230212 -5.33493
## levelGlobal:ehi -0.0333102 0.0228331 -1.45886
## fieldRVF:levelGlobal:ehi 0.0666075 0.0323174 2.06104
##
## Correlation of Fixed Effects:
## (Intr) fldRVF lvlGlb ehi flRVF:G flRVF: lvlGl:
## fieldRVF -0.155
## levelGlobal -0.156 0.506
## ehi -0.064 0.010 0.010
## fldRVF:lvlG 0.110 -0.713 -0.706 -0.007
## fieldRVF:eh 0.010 -0.067 -0.033 -0.154 0.047
## levelGlbl:h 0.010 -0.033 -0.065 -0.156 0.046 0.506
## fldRVF:lvG: -0.007 0.047 0.046 0.110 -0.065 -0.712 -0.706
Accuracy
Plots

Statistics
Model accuracy as a binomial effect of field, level, and EHI
(continuous):
acc_ehi_model <- glmer( rt ~ field*level*ehi + (1 | subject), family = "binomial" )
| npar |
AIC |
BIC |
logLik |
deviance |
Chisq |
Df |
p.value |
| 8 |
39,111.468 |
39,188.189 |
−19,547.734 |
39,095.468 |
- |
- |
- |
| 9 |
39,113.409 |
39,199.72 |
−19,547.704 |
39,095.409 |
0.059 |
1 |
.808 |
| field_consec |
level_consec |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| RVF - LVF |
Local - Global |
0.0002 |
0.0007 |
Inf |
−0.0013 |
0.0017 |
0.2491 |
.803 |
| contrast |
estimate |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF Global - LVF Local |
−0.001 |
0.0006 |
Inf |
−0.0021 |
0.0001 |
−1.8003 |
.072 |
| RVF Global - RVF Local |
−0.0012 |
0.0005 |
Inf |
−0.0022 |
−0.0002 |
−2.3594 |
.018 |
| field |
level |
ehi.trend |
SE |
df |
asymp.LCL |
asymp.UCL |
z.ratio |
p.value |
| LVF |
Global |
−0.0007 |
0.0007 |
Inf |
−0.002 |
0.0006 |
−1.0258 |
.305 |
| RVF |
Global |
−0.0006 |
0.0006 |
Inf |
−0.0018 |
0.0006 |
−0.9557 |
.339 |
| LVF |
Local |
0.0003 |
0.0006 |
Inf |
−0.0008 |
0.0014 |
0.5793 |
.562 |
| RVF |
Local |
0.0006 |
0.0006 |
Inf |
−0.0005 |
0.0017 |
1.0666 |
.286 |
| field_consec |
level_consec |
ehi |
odds.ratio |
SE |
df |
asymp.LCL |
asymp.UCL |
null |
z.ratio |
p.value |
| RVF / LVF |
Local / Global |
-100 |
1.67 |
0.166 |
Inf |
1.374 |
2.028 |
1 |
5.164 |
<.0001 |
| RVF / LVF |
Local / Global |
0 |
1.701 |
0.101 |
Inf |
1.514 |
1.911 |
1 |
8.942 |
<.0001 |
| RVF / LVF |
Local / Global |
100 |
1.733 |
0.159 |
Inf |
1.448 |
2.074 |
1 |
5.996 |
<.0001 |
| contrast |
ehi |
odds.ratio |
SE |
df |
asymp.LCL |
asymp.UCL |
null |
z.ratio |
p.value |
| LVF Global / LVF Local |
-100 |
2.83 |
0.209 |
Inf |
2.341 |
3.422 |
1 |
14.075 |
<.0001 |
| RVF Global / RVF Local |
-100 |
1.695 |
0.112 |
Inf |
1.429 |
2.01 |
1 |
7.953 |
<.0001 |
| LVF Global / LVF Local |
0 |
2.561 |
0.113 |
Inf |
2.287 |
2.868 |
1 |
21.336 |
<.0001 |
| RVF Global / RVF Local |
0 |
1.506 |
0.06 |
Inf |
1.359 |
1.668 |
1 |
10.266 |
<.0001 |
| LVF Global / LVF Local |
100 |
2.317 |
0.157 |
Inf |
1.947 |
2.758 |
1 |
12.409 |
<.0001 |
| RVF Global / RVF Local |
100 |
1.337 |
0.083 |
Inf |
1.141 |
1.567 |
1 |
4.697 |
<.0001 |
| field |
level |
ehi |
prob |
asymp.LCL |
asymp.UCL |
| LVF |
Global |
−100 |
0.983 |
0.98 |
0.986 |
| RVF |
Global |
−100 |
0.974 |
0.97 |
0.978 |
| LVF |
Local |
−100 |
0.953 |
0.947 |
0.96 |
| RVF |
Local |
−100 |
0.957 |
0.951 |
0.963 |
| LVF |
Global |
0 |
0.982 |
0.98 |
0.984 |
| RVF |
Global |
0 |
0.973 |
0.97 |
0.975 |
| LVF |
Local |
0 |
0.955 |
0.951 |
0.959 |
| RVF |
Local |
0 |
0.959 |
0.956 |
0.963 |
| LVF |
Global |
100 |
0.981 |
0.977 |
0.983 |
| RVF |
Global |
100 |
0.971 |
0.967 |
0.975 |
| LVF |
Local |
100 |
0.956 |
0.95 |
0.962 |
| RVF |
Local |
100 |
0.962 |
0.956 |
0.967 |
\[
log(1.73) = .548
\] \[
log(1.67) = .513
\] \[
log(1.73) - log(1.67) = .0353
\] \[
.0353 / 200 = -0.000185 logodds / EHI unit
\] The model estimates that a strong right hander (EHI +100) will
have 1.73/1.67 = 1.04 greater odds of correctness for LVF global stimuli
versus a strong left hander (EHI -100). Each unit change in EHI
(-100:100) corresponds to a 0.0002 (logodds) difference
in LVF global bias. This matches the slope estimate given by the summary
function:
summary(acc_model_ehi)
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: correct ~ field * level * ehi + (1 | subject)
## Data: aah_for_acc_ehi_model
##
## AIC BIC logLik deviance df.resid
## 39113.4 39199.7 -19547.7 39095.4 108023
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -11.748088 0.117364 0.168282 0.238851 1.067892
##
## Random effects:
## Groups Name Variance Std.Dev.
## subject (Intercept) 1.05841 1.02879
## Number of obs: 108032, groups: subject, 844
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 3.9930184017 0.0532670291 74.96229 < 2e-16 ***
## fieldRVF -0.4209327473 0.0474500751 -8.87107 < 2e-16 ***
## levelLocal -0.9403339363 0.0440725615 -21.33604 < 2e-16 ***
## ehi -0.0006744722 0.0006575342 -1.02576 0.305005
## fieldRVF:levelLocal 0.5311871060 0.0594032015 8.94206 < 2e-16 ***
## fieldRVF:ehi 0.0000955515 0.0005978575 0.15982 0.873020
## levelLocal:ehi 0.0009994867 0.0005551631 1.80035 0.071806 .
## fieldRVF:levelLocal:ehi 0.0001864551 0.0007484763 0.24911 0.803273
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) fldRVF lvlLcl ehi flRVF:L flRVF: lvlLc:
## fieldRVF -0.528
## levelLocal -0.575 0.636
## ehi -0.084 0.058 0.064
## fldRVF:lvlL 0.423 -0.799 -0.742 -0.046
## fieldRVF:eh 0.057 -0.105 -0.069 -0.538 0.084
## levelLocl:h 0.063 -0.069 -0.090 -0.583 0.066 0.635
## fldRVF:lvL: -0.045 0.084 0.066 0.430 -0.081 -0.799 -0.741
## optimizer (Nelder_Mead) convergence code: 0 (OK)
## Model failed to converge with max|grad| = 0.00445801 (tol = 0.002, component 1)
## Model is nearly unidentifiable: very large eigenvalue
## - Rescale variables?